EP 2 657 691 A1 describes a sensor device including a capacitive humidity sensor disposed on an integrated signal-processing component. The signal-processing component further has a temperature sensor integrated therewith. In order to protect such a sensor device from damage and to enable automated mounting thereof, for example, on a circuit board, the signal-processing component is usually placed on a support element (die pad) of a system carrier (lead frame) and provided with a suitable encapsulation (mold). In addition to the support element, the system carrier also includes connection contacts (leads) for electrical contacting of the signal-processing component. With regard to such systems, reference may be made, for example, to DE 20 2014 102 842 U1.